[General] The electron as a point particle: the experimental evidence.

[John Williamson]

Dear Ladies and Gentlemen,
This is a quick note in the spirit of a club both Martin and I belong to, the fanaten, a science study club of which Martin and I were founder members a quarter of a century ago. It is still going strong with regular mutual educational seminars. I do not attend, or contribute, as often as I would like – because I no longer live in Holland. This stuff could form the basis of talk to them at some point – what do you think Martin? Within the context here, it is intended to be simply educational. The main aim is to discuss whether or not the electron may, or may not, be a point. The discussion here is primarily on the basis of two experiments I carried out personally. There are many more in the literature – including those an the difference between centre of charge and centre of spin which have become current (see refs in other paper I sent – the one that is too dangerous for arXiv!).
Though current work seems to focus on theory I should reveal that I do not see myself as, primarily a theorist. Firstly, a natural philosopher, secondly an engineer, and only thirdly a (not very good) theorist. I think my theory is ok, in theory. It is just not very good in practice. I sometimes think I could make a sign error in signing my name. Martin is much better – think I have only found a sign error for him once!
 Anyway, for much of my career I was an experimentalist and engineer. My job at Philips was to propose and design new devices, to build and develop a measurement facility for them, to carry out the actual experiments and to interpret the results. I designed a couple of devices more than a quarter of a century ago. One of these was the “quantum point contact”, the other the “single electron electrometer” or “single electron pump”. These were pretty successful in taking science forwards at the time – the first (mostly with Henk van Houten or Bart van Wees as “first” author) pretty much took over the lions share of articles at solid state conferences at the time. The second – driven by the excellent Leo Kouwenhoven – continues to make significant impact today. In such experiments we looked at electrons in the solid state. Often single electrons in the solid state. This is why I know so much about them and the real meaning of their experimental properties in this regime: I carried out a good number of the seminal experiments personally.
The attached paper is one of these. My usual-co-authors declined to be involved with this particular one, partly because they found it a bit weird (and possibly even dirty). Timmering made the device, Foxon and Harris grew the (best in the world) material, and the excellent Kees Harmans was an all-round good guy from Delft . My role was the initial conception of the device, the optimisation of the measurement electronics and cryogenics, the (late night) experimental measurements and the interpretation of the results. Having said this, my initial  - and continuing - interpretation, did not make it into the actual paper. Parts were taken out on the insistence of more influential people in the group – mainly Henk, who said that “mensen zullen het niet begrijpen” (people will have trouble understanding it). Others were removed by referees. The final humiliation was that Physical review insisted on changing the title to include the word “contours” in place of the word “landscape”. The word “contours”, as you will note if you read it, appears only once in the article: in the title. The abstract, luckily, remained un-bowdlerised.  No matter- the experiment itself was sound and I am still here to say now what I think it really means. Also there is a typo at the bottom of page 7677 about the shifting of odd models – just to poke a bit of fun.
The experiment allowed the (landscape of the) lateral charge profile of single quantum-confined electrons, at a current low enough that they came over one at a time,  to inter-act with the (landscape of the) locality of the quantum point contact. The electron landscape was that familiar from quantum mechanics textbooks, with a single lobe for one half wavelength , a double lobe for two, three for three and so on. The observed quantised conductance depends on that number with 2 units of conductance (for spin up and spin down) per quantum mechanical sub-band. What the experiment shows, is that the charge profile of individual electrons in the solid state is, experimentally, spread over a few tens of nanometres. This charge interferes with that of the crystal charge distribution in such a way as to exclude certain sub-bands from transmission. These objects are BIG. The effective electron charge distribution is similar to that which one would expect from the interpretation of wave-mechanics. In that interpretation the biggest electron in a single crystal metal sliver is twice as big as the sliver (folded over on itself as it moves back and forth in a single-wavelength standing mode). Electrons in the solid state really do (experimentally) blow up to, literally, macroscopic sizes.
If that does not give the lie to the concept that the “electron is a point”  - I do not know what will.
Let me come back to another field in which I was personally involved and the experimental “proof” that the electron is measured to be a point in high-energy scattering experiments. This belief is widely held- even amongst experimental high-energy professionals. The theoretical wing believes implicitly this as one of the major commandments about the fundamental nature of the electron. Completely undeterred by the fact that they can all calculate that this cannot be the case from simple energy considerations, they will consider any suggestion to the contrary dangerous and delusional. I think the reason is that the electron is considered a point in the (well tested) quantum electrodynamics. Well tested it may be, but this is to confuse theory with reality. It is also to place old classical theory of mundane things such as field and energy as of no consequence when compared to big- sexy new field theory (QED). If you want a good laugh you should listen to some of these guys trying to argue with me in person. They lose. Fast.
This is because I am quite lucky in that, not only to I understand both QED and classical physics, but also I was one of the physicists who carried out the actual experiments. This means that I am in a position to not only suspect this is all bullshit, but also to know precisely why. It then becomes no contest: think Harrison Ford – they whip –me gun.
The fact of the matter is that the electron is observed to be point-like and not to be a point. That is the point. Any spherically symmetric distribution of energy-conserving objects will act in this way. The energy conservation ensures that the forces are inverse square and the corresponding potentials 1/r. Any distribution of these- if itself spherically symmetric, has a point-like interaction.  I teach this stuff in second year maths. Its easy. It is in 19th century textbooks. It is probably in Newton’s “Principia” – though I have not looked. That stuff has not gone away just because Richard Feynmann thought of a (very neat!) way of removing some calculational difficulties in electrodynamics
An analogy is the gravitational interaction. It too is inverse square in force and hence 1/r in potential. Spherical objects, such as the earth (roughly) act under gravitation as though their mass was concentrated at a point. If you do not believe me just try doing the integrations – they are not hard. This is just Newtonian gravitation. If you think this proves the earth is therefore a point just try looking out of the window. It really is this stupid!
Also what goes into QED is not, essentially, that the electron is a point. What goes in is that electrons emit photons with a certain probability (about 1/137). The point bit arises because of problems in the interpretation of the detail of this – the renormalisation scheme. This deals with the infinites by simple dividing them out. We need something better. A reason that the required length scale is (as Dirac pointed out) lambdac/4 pi. By a strange co-incidence this is just the characteristic length scale in the Martin-John model. Funny huh?
Ok … that is enough for now. Need to get back to thinking about important things like organising an exam on vectors and complex numbers ….
Cheers,
- John Williamson.




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